Time-Dependent Scalar Fields in Modified Gravities in a Stationary Spacetime

Abstract

Most no-hair theorems involve the assumption that the scalar field is independent of time. Recently in [Phys. Rev. D90 (2014) 041501(R)] the existence of time-dependent scalar hair outside a stationary black hole in general relativity was ruled out. We generalize this work to modified gravities and non-minimally coupled scalar field with an additional assumption that the spacetime is axisymmetric. It is shown that in higher-order gravity such as metric $f(R)$ gravity the time-dependent scalar hair doesn't exist. While in Palatini $f(R)$ gravity and non-minimally coupled case the time-dependent scalar hair may exist.

6 pages, no figures

References in corpus (6)

• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Explosion and final state of an unstable Reissner-Nordstrom black hole
• Electrically charged black hole with scalar hair
• Stationary Black Holes with Time-Dependent Scalar Fields
• Exact Black Hole Formation in Asymptotically (A)dS and Flat Spacetimes
• The significance of matter coupling in f(R) gravity

Cited by in corpus (4)

• Symmetry of Brans-Dicke gravity as a novel solution-generating technique
• Asymptotically flat black holes with scalar hair: a review
• No-hair theorems for non-canonical self-gravitating static multiple scalar fields
• Effective Field Theory of Hairy Black Holes and Their flat/dS limit